Solve for $x$ and $y$ using elimination. ${-3x+6y = 57}$ ${-3x+5y = 47}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-3x+6y = 57}$ $3x-5y = -47$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+6y = 57}\thinspace$ to find $x$ ${-3x + 6}{(10)}{= 57}$ $-3x+60 = 57$ $-3x+60{-60} = 57{-60}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-3x+5y = 47}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(10)}{= 47}$ ${x = 1}$